Symmetries of geometric flows

By applying the theory of group-invariant solutions we investigate the symmetries of Ricci flow and hyperbolic geometric flow both on Riemann surfaces. The warped products on $\mathcal {S}^{n+1}$ of both flows are also studied.Comment: 27 page

Long time well-posdness of the Prandtl equations in Sobolev space

In this paper, we study the long time well-posedness for the nonlinear Prandtl boundary layer equation on the half plane. While the initial data are small perturbations of some monotonic shear profile, we prove the existence, uniqueness and stability of solutions in weighted Sobolev space by energy methods. The key point is that the life span of the solution could be any large $T$ as long as its initial date is a perturbation around the monotonic shear profile of small size like $e^{-T}$. The nonlinear cancellation properties of Prandtl equations under the monotonic assumption are the main ingredients to establish a new energy estimate.Comment: In this version, reviser some typos, 43 page

AutoEncoder Inspired Unsupervised Feature Selection

High-dimensional data in many areas such as computer vision and machine learning tasks brings in computational and analytical difficulty. Feature selection which selects a subset from observed features is a widely used approach for improving performance and effectiveness of machine learning models with high-dimensional data. In this paper, we propose a novel AutoEncoder Feature Selector (AEFS) for unsupervised feature selection which combines autoencoder regression and group lasso tasks. Compared to traditional feature selection methods, AEFS can select the most important features by excavating both linear and nonlinear information among features, which is more flexible than the conventional self-representation method for unsupervised feature selection with only linear assumptions. Experimental results on benchmark dataset show that the proposed method is superior to the state-of-the-art method.Comment: accepted by ICASSP 201